Math (algebra)

Always use reverse Bodmas:

This means that addition goes to the other side first and subtraction too. When solving equations, if you need to move a term from one side to the other, perform any additions or subtractions first before addressing other operations. This principle helps to maintain the integrity of the equation and ensures accurate results.

If you have an exponent and brackets on one side, then move the exponent first.

^-5 equals to ^1/-5

^1/5 = ^ 5

More on Operations:

  1. Brackets: Always begin by solving anything inside brackets. This includes terms grouped together, like (x + 5) or (2y - 3). Remember, resolving brackets first is crucial as it can significantly affect the outcome of your calculations.

  2. Orders (Powers and Roots): After brackets, the next step is to resolve any powers or roots. This entails calculating exponents such as a^3 or square roots. If you have an exponent on one side and you need to move it across the equation, you must also adjust the sign accordingly; for example, if you move from a^{1/5}, it becomes a^5 when on the opposite side.

  3. Division and Multiplication: Next, perform any division and multiplication operations from left to right. It’s important to recognize that division is the inverse of multiplication, so changing the position of a term in an equation will also necessitate the corresponding change of operation.

  4. Addition and Subtraction: Lastly, handle any addition and subtraction actions from left to right. These operations are considered the lowest priority in the BODMAS/BIDMAS hierarchy, but they are still essential for arriving at the correct answer.

Powers and Their Distribution:

Multiplication distributes over addition and subtraction: For example, in the expression a(b + c), you would multiply a by both b and c to get ab + ac. This applies similarly in subtraction: a(b - c) results in ab - ac.

Powers distribute over all terms, but in different methods: For example, when dealing with powers: (a^m)(a^n) = a^(m+n) and (a^m) / (a^n) = a^(m-n). However, when handling and distributing an expression like (a + b)^2, it does not expand as a^2 + b^2, but rather as a^2 + 2ab + b^2. This distinction is essential for simplifying polynomial expressions accurately.

Basic Rules for Equations:

  • Equality: Whenever you perform a mathematical operation on one side of the equation, you must do the exact same operation on the other side to maintain balance and equality in the equation.

  • Combining Like Terms: To simplify expressions effectively, always combine like terms, which involves grouping terms that have the same variable or constant. This makes calculations easier and helps in consolidating your answer.

How to Solve Equations:

  1. Begin by simplifying both sides of the equation as much as possible using BODMAS/BIDMAS rules. This step is crucial in weakening the complexity of the equation you're working with.

  2. Utilize addition or subtraction to isolate the variable on one side of the equation, adjusting other terms as necessary to achieve this isolation successfully.

  3. If necessary, apply multiplication or division to isolate and solve for the variable. This may involve further adjustments of powers or transferring terms across the equation’s equal sign appropriately.

  4. Check Your Solution: After finding a potential solution, always substitute it back into the original equation. This verification step is essential in confirming that the solution you derived is indeed correct and satisfies the original equation.